in 2012, the general social survey included a question that asked participants how many hours they worked a week. do males work
1 answer:
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Answer:
Part 1) The vertex is the point (-83,-9)
Part 2) The focus is the point (-82.75,-9)
Part 3) The directrix is
Step-by-step explanation:
step 1
Find the vertex
we know that
The equation of a horizontal parabola in the standard form is equal to
where
p≠ 0.
(h,k) is the vertex
(h + p, k) is the focus
x=h-p is the directrix
In this problem we have
Convert to standard form
so
This is a horizontal parabola open to the right
(h,k) is the point (-83,-9)
so
The vertex is the point (-83,-9)
step 2
we have
<em>Find the value of p</em>
<em>Find the focus</em>
(h + p, k) is the focus
substitute
(-83+1/4,-9)
The focus is the point (-82.75,-9)
step 3
Find the directrix
The directrix of a horizontal parabola is
substitute
Answer:
And we can find this probability with the following difference and using the normal standard table or excel we have:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with the following difference and using the normal standard table or excel we have: